There was a problem to make a shadow and reflection of the object on invisible plane using Mental Ray's Matte/Shadow/Reflection material. After browsing and reading stuff I've found a good Jeff Patton's idea for Maya which I adopted for 3DS Max.
So, as usual use a plane with Matte/Shadow/Reflection material. To make it invisible use Environment background Switcher map on it's Camera Mapped background slot and on Environment slot of a scene, for example I had an HDRI map and gray background. Gray background is generated with Composite map, though the colour of the back can be set to any colour, read on to know why.
Do not forget to enable Process background and environment map in Exposure Control to avoid black plane (due to difference in exposure control).